Volumetric Scatter ignoring World lighting
I've managed to get this working - the problem only occurs when Surface Multiple Importance Sampling is not enabled for the World.

Here I have two Suzannes - one with Diffuse (the one on the Right) and one with Volumetrics to mimic the diffuse (with the Diffuse at 20% grey to produce a similar shading).

With Multiple Importance of the World disabled (the default) the volumetric material ignores the (red) World illumination :



With Multiple Importance Sampling of the World enabled, the volumetric material is correctly illuminated by the world :



Also, with Multiple Importance enabled, the Ray Visibility works as it should - enabling and disabling the effect on the volumetric scatter.

I don't know enough about the Multiple Importance Sampling to know if this is expected behaviour or what the downsides of enabling Multi-Importance (if any) are, but it fixed the problem for my situation.